Why Operating Leverage Multiplies the Percentage Change in Profit
Summary
The document explains why a percentage increase in sales can produce a larger percentage increase in operating profit when a business has fixed operating costs. It defines operating leverage as contribution margin divided by operating profit, with contribution margin equal to quantity sold times the difference between price and average variable cost. If price and variable cost per unit remain fixed, a percentage rise in sales corresponds to the same percentage rise in quantity.
The explanation substitutes the higher quantity into the profit equation, which subtracts fixed operating costs from total contribution margin. Comparing new profit with initial profit shows that the percentage change equals the sales percentage change multiplied by the operating leverage ratio. The result is an algebraic identity under those assumptions, rather than an empirical finding. It depends on fixed costs, price, and unit variable costs staying constant over the change; the document does not discuss nonlinear costs or changes in product mix.
Key ideas
- Operating leverage is contribution margin divided by operating profit.
- With price and unit variable cost fixed, a percentage change in sales implies the same percentage change in quantity.
- Fixed operating costs cause profit to change by a larger percentage than contribution margin.
- The leverage relationship assumes costs and prices do not change during the sales shift.
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# Operating Leverage Interpretation
# Operating Leverage Interpretation
Operating Leverage is the ratio of Contribution margin and operating income(proxy of profit).
So, Operating Leverage = [Sales-Variable Cost]/[Profit] = Quantity*(Price-AVC)/Profit
Many literature including investopedia, CFA curriculum suggests that if operating leverage is k, then if sales go up by a%, the profit will go up by k times a% = ak%
But, if I use the formula, Sales going up by a% implies, quantity going up by a% as price and AVC are fixed. Then, how come Profit will increase by ak%?
## Answer by emot (score 3, accepted)
https://quant.stackexchange.com/a/66400
Operating leverage $k$: $$k=\frac{Quantity*(Price-AVC)}{Profit}$$ but profit (actually operating profit) is: $$Profit=Quantity*(Price-AVC)-FixOpCosts$$ If quantity sold increases by $a\%$ then our new profit is: $$Profit_{new}=Quantity*(Price-AVC)(1+a)-FixOpCosts$$ Percentage change in Profit is: $$Profit_{new}/Profit-1$$ Then you are basically asking if $$ka\stackrel{?}{=}Profit_{new}/Profit-1$$
It is just simple algebra to show that it holds $$ka\stackrel{?}{=}\frac{Profit_{new}}{Profit}-1$$ $$ka\stackrel{?}{=}\frac{Quantity*(Price-AVC)(1+a)-FixOpCosts}{Quantity*(Price-AVC)-FixOpCosts}-1$$ $$ka\stackrel{?}{=}\frac{Quantity*(Price-AVC)(1+a)-FixOpCosts}{Quantity*(Price-AVC)-FixOpCosts}-\frac{Quantity*(Price-AVC)-FixOpCosts}{Quantity*(Price-AVC)-FixOpCosts}$$
$$ka\stackrel{?}{=}\frac{Q(Price-AVC)a}{Q(Price-AVC)-FixOpCosts}$$ Given our definition of k we have: $$\frac{Quantity(Price-AVC)}{Profit}a\stackrel{?}{=}\frac{Q(Price-AVC)a}{Q(Price-AVC)-FixOpCosts}$$
Given our definition of $Profit$ we see that it in fact holds: $$ka{=}\frac{Profit_{new}}{Profit}-1$$
Hope that helps.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.